Solve (sqrt{39}+sqrt{3})(3-sqrt{13})

$$( \sqrt { 39 } + \sqrt { 3 } ) ( 3 - \sqrt { 13 } )$$

Evaluate

$$2\left(\sqrt{39}-5\sqrt{3}\right)\approx -4.830512079$$

Solution Steps

Apply the distributive property by multiplying each term of \sqrt{39}+\sqrt{3} by each term of 3-\sqrt{13}.

$$3\sqrt{39}-\sqrt{39}\sqrt{13}+3\sqrt{3}-\sqrt{3}\sqrt{13}$$

Factor 39=13\times 3. Rewrite the square root of the product \sqrt{13\times 3} as the product of square roots \sqrt{13}\sqrt{3}.

$$3\sqrt{39}-\sqrt{13}\sqrt{3}\sqrt{13}+3\sqrt{3}-\sqrt{3}\sqrt{13}$$

Multiply \sqrt{13} and \sqrt{13} to get 13.

$$3\sqrt{39}-13\sqrt{3}+3\sqrt{3}-\sqrt{3}\sqrt{13}$$

Combine -13\sqrt{3} and 3\sqrt{3} to get -10\sqrt{3}.

$$3\sqrt{39}-10\sqrt{3}-\sqrt{3}\sqrt{13}$$

To multiply \sqrt{3} and \sqrt{13}, multiply the numbers under the square root.

$$3\sqrt{39}-10\sqrt{3}-\sqrt{39}$$

Combine 3\sqrt{39} and -\sqrt{39} to get 2\sqrt{39}.

$$2\sqrt{39}-10\sqrt{3}$$